Nonstationary response statistics of fractional oscillators to evolutionary stochastic excitation

2021 ◽  
pp. 105962
Author(s):  
Qianying Cao ◽  
Sau-Lon James Hu ◽  
Huajun Li
Keyword(s):  
Stochastic Excitation ◽  
Nonstationary Response

On the Nonstationary Response of Stochastically Excited Secondary Systems

1987 ◽  
Vol 54 (3) ◽  
pp. 688-694 ◽  
Author(s):  
W. D. Iwan ◽  
K. S. Smith
Keyword(s):  
Closed Form Expression ◽  
Primary System ◽  
Mean Square ◽  
Stochastic Excitation ◽  
Secondary System ◽  
Form Expression ◽  
Combined System ◽  
Nonstationary Response ◽  
Secondary Systems ◽  
The Mean

The envelope response of a secondary system is derived for the case where the primary system is subjected to nonstationary stochastic excitation. An approximate closed form expression for the mean square envelope response is obtained for the case of transient response to stationary excitation when the primary and secondary systems are noninteracting. When the combined system is classically damped, the effect of the interaction is described by the introduction of an equivalent noninteracting system. The analytical results are compared with results of numerical simulations.

Wideline 2H -NMR Spectroscopy and Imaging of Solids

1994 ◽  
Vol 49 (1-2) ◽  
pp. 19-26 ◽  
Author(s):  
B. Blümich
Keyword(s):  
Nmr Spectroscopy ◽  
Excitation Power ◽  
Magic Angle Spinning ◽  
Magic Angle ◽  
2H Nmr ◽  
Stochastic Excitation ◽  
2H Nmr Spectroscopy ◽  
Spatially Inhomogeneous ◽  
Recent Developments ◽  
Angle Spinning

Abstract Recent developments, focussing on reduction of the rf excitation power by stochastic excitation, on improvements in sensitivity and excitation bandwidth by magic angle spinning, and on combining wideline spectroscopy with spatial resolution for investigations o f spatially inhomogeneous objects are reviewed.

Wave propagation dynamics in a fractional Zener model with stochastic excitation

2020 ◽  
Vol 23 (6) ◽  
pp. 1570-1604
Author(s):  
Teodor Atanacković ◽  
Stevan Pilipović ◽  
Dora Seleši
Keyword(s):  
Wave Propagation ◽  
Constitutive Equation ◽  
Equations Of Motion ◽  
Weak Form ◽  
Stochastic Excitation ◽  
Expansion Theorem ◽  
Zener Model ◽  
Dissipation Inequality ◽  
Regularity Properties ◽  
Fractional Zener Model

Abstract Equations of motion for a Zener model describing a viscoelastic rod are investigated and conditions ensuring the existence, uniqueness and regularity properties of solutions are obtained. Restrictions on the coefficients in the constitutive equation are determined by a weak form of the dissipation inequality. Various stochastic processes related to the Karhunen-Loéve expansion theorem are presented as a model for random perturbances. Results show that displacement disturbances propagate with an infinite speed. Some corrections of already published results for a non-stochastic model are also provided.

scholarly journals Linearization threshold condition and stability analysis of a stochastic dynamic model of one-machine infinite-bus (OMIB) power systems

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Lijuan Li ◽  
Yongdong Chen ◽  
Bin Zhou ◽  
Hongliang Liu ◽  
Yongfei Liu
Keyword(s):  
Power Systems ◽  
Power System ◽  
Dynamic Model ◽  
Threshold Model ◽  
Security Evaluation ◽  
Stochastic Dynamic ◽  
Threshold Condition ◽  
Stochastic Excitation ◽  
Predictor Corrector ◽  
One Machine

AbstractWith the increase in the proportion of multiple renewable energy sources, power electronics equipment and new loads, power systems are gradually evolving towards the integration of multi-energy, multi-network and multi-subject affected by more stochastic excitation with greater intensity. There is a problem of establishing an effective stochastic dynamic model and algorithm under different stochastic excitation intensities. A Milstein-Euler predictor-corrector method for a nonlinear and linearized stochastic dynamic model of a power system is constructed to numerically discretize the models. The optimal threshold model of stochastic excitation intensity for linearizing the nonlinear stochastic dynamic model is proposed to obtain the corresponding linearization threshold condition. The simulation results of one-machine infinite-bus (OMIB) systems show the correctness and rationality of the predictor-corrector method and the linearization threshold condition for the power system stochastic dynamic model. This study provides a reference for stochastic modelling and efficient simulation of power systems with multiple stochastic excitations and has important application value for stability judgment and security evaluation.

Bifurcations of a Nonlinear Two-Degree-of-Freedom System Under Narrow-Band Stochastic Excitation

1992 ◽  
Vol 114 (1) ◽  
pp. 24-31
Author(s):  
R. Lin ◽  
K. Huseyin ◽  
C. W. S. To
Keyword(s):  
Relaxation Time ◽  
Correlation Time ◽  
Averaging Method ◽  
Narrow Band ◽  
Singularity Theory ◽  
Random Parameter ◽  
Degree Of Freedom ◽  
Stochastic Excitation ◽  
Static Approach ◽  
Two Degree Of Freedom

In this paper, bifurcations of a nonlinear two-degree-of-freedom system subjected to a narrow-band stochastic excitation are investigated. Under the assumption that the correlation time greatly exceeds the relaxation time, a quasi-static approach combined with averaging method is adopted to obtain the bifurcation equations, and the singularity theory is applied to analyze the bifurcations. It is demonstrated that bifurcation patterns jump from one to another due to the influence of a random parameter. The probabilities of the jumping bifurcation patterns are given.

Nonstationary Response of a Two-Degrees-of-Freedom Nonlinear Ship Model Under Modulated Excitation

1995 ◽  
Author(s):  
Ruigui Pan ◽  
Huw G. Davies
Keyword(s):  
Degrees Of Freedom ◽  
Stability Boundary ◽  
Period Doubling ◽  
Approximate Solutions ◽  
Loss Of Stability ◽  
Two Degrees Of Freedom ◽  
Ship Model ◽  
Nonstationary Response ◽  
Period 2 ◽  
The Stability

Abstract Nonstationary response of a two-degrees-of-freedom system with quadratic coupling under a time varying modulated amplitude sinusoidal excitation is studied. The nonlinearly coupled pitch and roll ship model is based on Nayfeh, Mook and Marshall’s work for the case of stationary excitation. The ship model has a 2:1 internal resonance and is excited near the resonance of the pitch mode. The modulated excitation (F0 + F1 cos ωt) cosQt is used to model a narrow band sea-wave excitation. The response demonstrates a variety of bifurcations, loss of stability, and chaos phenomena that are not present in the stationary case. We consider here the periodically modulated response. Chaotic response of the system is discussed in a separate paper. Several approximate solutions, under both small and large modulating amplitudes F1, are obtained and compared with the exact one. The stability of an exact solution with one mode having zero amplitude is studied. Loss of stability in this case involves either a rapid transition from one of two stable (in the stationary sense) branches to another, or a period doubling bifurcation. From Floquet theory, various stability boundary diagrams are obtained in F1 and F0 parameter space which can be used to predict the various transition phenomena and the period-2 bifurcations. The study shows that both the modulation parameters F1 and ω (the modulating frequency) have great effect on the stability boundaries. Because of the modulation, the stable area is greatly expanded, and the stationary bifurcation point can be exceeded without loss of stability. Decreasing ω can make the stability boundary very complicated. For very small ω the response can make periodic transitions between the two (pseudo) stable solutions.

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